Advanced Geometry

Picking up where the standard introductory high school geometry class left off, Advanced Geometry is a one-semester course that investigates advanced topics in Euclidean Geometry. We study triangle centers, incircles and excircles, the 9-point-circle, the power of a point, the radical axis of two circles, Simson lines, Ptolemy's Theorem, and the Fermat Point. We study the transformational geometry of translations, rotations, reflections, half-turns, dilations, and inversion in a circle. After studying the theorems of Menelaus, Pappus, Desargues, Pascal, and Brianchon, we conclude the class with a full investigation of Projective Geometry. 

With a delightful textbook as our guide, we create the geometric figures live in class using Geogebra, a dynamic geometry software. This is a class with lots of discussion and student participation, challenging, but also very fun.